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Cavity quantum electrodynamics (QED) provides a fundamental platform for implementing lightmatter interactions at the single-particle level, having been extensively investigated in fundamental physics and quantum information. Recent advances in parametric squeezing techniques have demonstrated remarkable capabilities for exponentially enhancing coherent coupling between an atom and a cavity. However, the full extent of manipulating quantum optical phenomena using these techniques still requires further exploration. This work systematically investigates the effects of optical parametric amplification on single-photon excited atom-cavity systems within a parametric driven cavity. In the proposed model, optical parametric amplification converts the driving photons into a squeezed cavity mode, which can enhance the atom-cavity interaction to the strong coupling region. Through analytical derivation of atomic and cavity radiation spectra, we demonstrate that the optical parametric amplification can lead to the splitting of atomic radiation spectra, but produces negligible effects on spectral intensity. Conversely, the cavity transmission spectrum exhibits both pronounced splitting and nonlinear intensity amplification. Notably, when driving field intensity approaches critical region, the intensity of the cavity radiation spectrum can be significantly enhanced. The underlying mechanism originates from parametric driving amplification, which converts the driving light into a squeezed cavity mode. When this squeezed mode is mapped back to the original mode of the cavity through Bogoliubov squeezing transformation, the pump photons in the squeezed cavity mode are converted into the radiation spectrum of the cavity, which leads to the amplification of the cavity radiation spectrum. This parametric enhancement protocol not only deepens fundamental understanding of engineered light-matter interactions but also establishes a practical framework for improving single-photon detection sensitivity in cavity-based quantum systems. These findings hold promising implications for quantum sensing and information processing applications.
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